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Coupling PDEs and SDEs: The Illustrative Example of the Multiscale Simulation of Viscoelastic Flows

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Multiscale Methods in Science and Engineering

Part of the book series: Lecture Notes in Computational Science and Engineering ((LNCSE,volume 44))

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Summary

We present an overview of models which couple a partial differential equation with a stochastic differential equation posed at each point of the physical space. Such systems in particular arise in multiscale models of complex fluids, but also in the modeling of emission and transport of photons for example. For each case, we mention the mathematical and numerical issues and indicate the main results obtained so far.

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Author information

Authors and Affiliations

  1. Ecole Nationale des Ponts et Chaussées, CERMICS, 6 & 8 Av. Pascal, 77455, Champs-sur-Marne, France

    Benjamin Jourdain, Claude Le Bris & Tony Lelièvre

Authors
  1. Benjamin Jourdain
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  2. Claude Le Bris
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  3. Tony Lelièvre
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Editor information

Editors and Affiliations

  1. Department of Numerical Analysis and Computer Science, Royal Institute of Technology, SE-10044, Stockholm, Sweden

    Björn Engquist  & Olof Runborg  & 

  2. Department of Information Technology, Uppsala University, Box 337, SE-75105, Uppsala, Sweden

    Per Lötstedt

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Jourdain, B., Le Bris, C., Lelièvre, T. (2005). Coupling PDEs and SDEs: The Illustrative Example of the Multiscale Simulation of Viscoelastic Flows. In: Engquist, B., Runborg, O., Lötstedt, P. (eds) Multiscale Methods in Science and Engineering. Lecture Notes in Computational Science and Engineering, vol 44. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-26444-2_7

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